Teaching

currently(Spring2020) i am teaching math 601 Algebraic topology

Math 601 Algebraic Topology （Spring 2020)

Instructor: Prof. Herman Gluck
Course description: Covering spaces and fundamental groups, van Kampen's theorem and classification of surfaces. Basics of homology and cohomology, singular and cellular; isomorphism with de Rham cohomology. Brouwer fixed point theorem, CW complexes, cup and cap products, Poincare duality, Kunneth and universal coefficient theorems, Alexander duality, Lefschetz fixed point theorem.
Office lolation: DRL 3C15
Homework solutions/comments:
Homework 2 Covering spaces
Homework 3 Retractions, Borsuk-Ulam Theorem, Fundamental Theorem of Algebra, Vector Fields and Fixed Points
HW 4 Computing fundamental groups
Homework 5 Covering space revisited
Homework 6 More Covering space

Math 500 Topology （Fall 2019)

Instructor: Leandro Lichtenfelz
Course description: This course covers point-set and algebraic topology. In point-set topology, we generalize the ideas of open sets, continuity, connectedness and compactness from analysis. Topology can be viewed as qualitative geometry; rather than paying attention to distances, curvature, and other quantitative properties of a space, we study the connectedness of the space, whether it has "holes," and so on. In algebraic topology, we build tools for converting problems in topology, where there is little structure, into problems in algebra, where there is a lot of structure.

Office hours: By appointments
Office lolation: DRL 3C15
Topics covered: Point set topology: metric spaces and topological spaces, compactness, connectedness, continuity, extension theorems, separation axioms, quotient spaces, topologies on function spaces, Tychonoff theorem. Algebraic topology: Fundamental groups and covering spaces, and related topics.

Math 370 Abstract algebra（spring 2018)

Instructor: Prof. Alexandre Kirillov
TA: Qingyun Zeng (Andy)
Course description: Math 370 covers group theory, group actions, symmetry, linear groups, and element od representation theory.

Office hours: MW 5:30pm-6:30am, and by appointments
Office lolation: DRL 3C17
Syllabus: PDF version
Textbook: Algebra by M. Artin

Recitation notes, handout, and additional materials
Week 1
  • Here's a short and concise notes of Group theory. If you plan to go to graduate school in math, I recommend Aluffi's Algebra: Chapter 0 which has more categorical flavor.

    • Week 2
  • Notes of the lab. Recommended reading: Sec. 1.1, 1.3, 1.4, 2.1, 8.1 in Group theory notes, and/or Sec 2.1-2.4 in Artin
  • Hint/solutions to HW1

    • Week 3
  • Notes for week 3. Recommended reading: Sec 1.2 and all of section 3 (Lagrange's theorem) in Group theory notes, and/or sec. 2.5, 2.6, 2.8, 2.9 in Artin. For those of you who have less experience about Proofs (introduced in MATH 203 Proving things), here's a short paper Introduction to mathematical arguments which might be helpful.
    • Week 4
  • Notes. Recommended reading: Sec 3.2, 4.1, 4.2 in Group theory notes, and/or Sec 2.10, 2.12 in Artin.
  • Some practice problems: Group theory practice problems 1

    • Math 314/514-402/403 advanced linear algebra（spring 2018)

    ! Important Update on 2017.01.16
    I have resigned from the teaching assistantship of MATH314/514 yesterday due to severe conflict between the instructor and me. I was not able to work under prejudice and discrimination.

    Instructor: Prof. Antonella Grassi
    TA: Qingyun Zeng (Andy)
    Course description: Math 314/514 covers Linear Algebra at the advanced level with a theoretical approach. Topics will include: Vector spaces, Basis and dimension, quotients; Linear maps and matrices; Determinants, Dual spaces and maps; Invariant subspaces, Cononical forms; Scalar products: Euclidean, unitary and symplectic spaces; Orthogonal and Unitary operators; Tensor products and polylinear maps; Symmetric and skew-symmetric tensors and exterior algebra.

    Office hours: MF 9:00pm-10:00am, and by appointments
    Office lolation: DRL 3C17
    Syllabus: See Canvas
    Textbook: Linear algebra by Hoffman and Kunze , and Liner algebra done wrong (updated 2017.9) by Sergei Treil

    Recitation notes, handout, and additional materials
    Week 1
  • Notes of Recitation 1 . Here is a brief summary of Chapter 1
  • Summary of Sec. 2.1-2.2 of Chapter 2


    • Math 500 Topology （Fall 2017)

    Instructor: Brian Weber
    Course description: This course covers point-set and algebraic topology. In point-set topology, we generalize the ideas of open sets, continuity, connectedness and compactness from analysis. Topology can be viewed as qualitative geometry; rather than paying attention to distances, curvature, and other quantitative properties of a space, we study the connectedness of the space, whether it has "holes," and so on. In algebraic topology, we build tools for converting problems in topology, where there is little structure, into problems in algebra, where there is a lot of structure.

    Office hours: By appointments
    Office lolation: DRL 3C17
    Topics covered: Point set topology: metric spaces and topological spaces, compactness, connectedness, continuity, extension theorems, separation axioms, quotient spaces, topologies on function spaces, Tychonoff theorem. Algebraic topology: Fundamental groups and covering spaces, and related topics.

    Math 241-910 Calculus IV （Summer 2017)

    Instructor: Qingyun Zeng (Andy)
    Course description: This course is an introduction to Partial Differential Equations (PDEs). Topics discussed in the course include: Heat, Wave and Laplace equations, Separation of Variables, Fourier series, Sturm-Liouville problems, Bessel functions and Fourier transform.

    Office hours: MTWR12:00pm-1:00pm, and by appointments
    Office lolation: DRL 3C17
    Textbook: Applied Partial Differential Equations: With Fourier Series and Boundary Value Problems, by Richard Haberman.

    Lecture notes
    Week 1
  • Lec 1 (May 22). We covered roughly Sec. 1.1-1.3 in Haberman. Here is a supplementary notes on ODEs.
  • Lec 2 (May 23). We covered Sec. 1.4-1.5 and Sec. 2.1-2.2. Here is an animation of 2D heat equation of Dirichelet boundary conditions (Prescribed temperature).
  • Lec 3 (May 24). We covered Sec. 2.3 and most of 2.4.
  • Lec 4 (May 25). We covered Sec 2.5, 3.1, and most of the 3.2.
    • Week 2
  • Memorial day (May 29) , no class. The Quiz 1 is on Tuesday this week.
  • Lec 5 (May 30). We covered Sec 3.3.1 today. The rest of the notes will be covered tomorrow and we will fininsh Chapter 3.
  • Lec 6 (May 31). We covered Sec 3.3.1-3.3.5, 3.6, 4.1-4.2 today. Tomorrow we will see more examples about wave equations.
  • Lec 7 (Jun 1). We covered Sec 4.3-4.4 and finished Chapter 4.
    • Week 3
  • Lec 8 (Jun 5). We covered Sec. 5.1-5.4 of Strum-Liouville problems. Here's an additional notes
  • Lec 9 (June 6). We covered Sec. 7.1-7.3 of Higher dumensional PDEs
  • Lec 10 (June 7). We covered Sec. 7.4-7.6: Mutidimensional eigenvalue problems
  • Lec 11 (June 8). We covered Sec. 7.7: Vibrating Circular Membrane and Bessel functions. Here's an additional notes on Bessel functions. Below is an demostration of vibrating circular membrane . Here's a real membrane video.
    • Week 4
  • Lec 12 (June 12). We covered Sec.7.9-7.10: Laplace equations in circlular cylinder, modified Bessel functions, Spherical problems and Legendre polynomials. Here's an additional notes on Laplace equation on a solid cylinder. Below is a video on spherical harmonics
  • Lec 13 (June 13). We covered Sec. 8.1-8.3, the begining of nonhomogeneous problems
  • Lec 14 (June 14). We covered Sec 8.3 eigenfunction expansions
  • Lec 15 (June 15). We covered Sec 8.6 Poisson equations and Sec 10.1-10.3 of Fourier transforms
  • Lec 16 (June 19). We covered Sec. 10.3.
  • Lec 17 (June 20) We covered Sec. 10.4 Fourier transform and heat equation, 10.6.1 1D Wave equation on an infinite interval, and 10.6.3 Laplace equation in a Half-plane. We will finish Fourier transfrom tomorrow and begin some topics in Funtions of Complex Variables.

    •  

    Homework

    Week 1
    1. May 22, Homework 1A. Due: May 25 (Thursday)
    2. May 23, Homework 1B. Due: May 25 (Thursday)
    3. May 24, Homework 2A. Due: May 30 (Tuesday)
    4. May 25, Homework 2B. Due: May 30 (Tuesday)
    week 2
    5. May 30, Homework 3A. Due: June 1 (Thursday)
    6. May 31, Homework 4A. Due: June 5 (Monday)
    7. June 1, Homework 4B. Due: June 5 (Monday)

    Week 3
    8. June 5, Homework 5A. Due: June 8 (Thursday)
    9. June 6, Homework 5B. Due: June 8 (Thursday)
    10. June 7, Homework 6A. Due: June 12 (Monday)
    11. June 8, Homework 6B. Due: June 12 (Monday)
    Week 4
    12. June 11. Homework 7A. Due: June 15 (Thursday)
    13. June 12. Homework 7B. Due: June 15 (Thursday)
    14. June 13. Homework 8A. Due: June 19 (Monday)
    15. June 14. Homework 8B. Due: June 19 (Monday)
    Week 5 (almost done!)
    16. June 19. Homework 9A. Due: June 22 (Thursday)
    17. June 20. Homework 9B. Due: June 22 (Thursday)

    Quizzes
    Quiz 0: knowledge check list
    Quiz 1 (May 30, Tuesday)
    Quiz 2 (June 5, Monday)
    Quiz 3 (June 12, Monday)
    Quiz 4 (June 19, Monday)

    Final Exam
    Final Exam (June 27, Tuesday)

    Past teaching:

    MATH 241 Spring 2017 as TA

    MATH 241 Fall 2017 as TA

    Homework & solutions.

    Homework Solutions some notes&material
    HW1 Full solutions by courtesy of Brandon Lin Notes on 1st order ODEs by Prof. Deturck
    HW2 solutions to HW1&2
    Full solutions by courtesy of Brandon Lin    		 Derivation of Heat equation in higer dimensions
    HW3 solutions to HW3
    Full solutions by courtesy of Brandon Lin    		 Fourier series examples
    HW4 solutions to HW4
    Full solutions by courtesy of Brandon Lin    		 Extra notes on Probelm 4.4.3 (solving a non-homogeneous 1D wave equation)
    HW5 Due Oct 21   Notes on Strum-Liouville eigenvalue problems
    Note on further applications of Bessel functions
    HW6 Due Oct 28